学步园

题意：BL == N (mod P)，并且p是素数

题解：

#include<cstdio>
#include<cmath>
#include<cstring>
using namespace std;

#define lint  __int64
#define MAXN 131071
struct HashNode { lint data, id, next; };
HashNode hash[MAXN<<1];
bool flag[MAXN<<1];
lint top;

lint gcd ( lint a, lint b )
{
    return b ? gcd ( b, a % b ) : a;
}

lint ext_gcd ( lint a, lint b, lint& x, lint& y )
{
    lint t, ret;
    if ( b == 0 )
    {
        x = 1, y = 0;
        return a;
    }
    ret = ext_gcd ( b, a % b, x, y );
    t = x; x = y; y = t - a / b * y;
    return ret;
}

lint mod_exp ( lint a, lint b, lint n )
{
    lint ret = 1;
    a = a % n;
    while ( b >= 1 )
    {
        if ( b & 1 )
            ret = ret * a % n;
        a = a * a % n;
        b >>= 1;
    }
    return ret;
}

void Insert ( lint index, lint num )
{
    lint k = num % MAXN;
    if ( flag[k] == false )
    {
        flag[k] = true;
        hash[k].id = index;
        hash[k].data = num;
        hash[k].next = -1;
        return;
    }
    while ( hash[k].next != -1 )
    {
        if ( hash[k].data == num ) return;
        k = hash[k].next;
    }
    if ( hash[k].data == num ) return;
    hash[k].next = ++top;
    hash[top].id = index;
    hash[top].data = num;
    hash[top].next = -1;
}

lint Find ( lint num )
{
    lint k = num % MAXN;
    if ( flag[k] == false ) return -1;
    while ( k != -1 )
    {
        if ( hash[k].data == num )
            return hash[k].id;
        k = hash[k].next;
    }
    return -1;
}

lint BabyStep_GiantStep ( lint A, lint B, lint C )
{
    top = MAXN; B %= C;
    lint tmp, i, x, y, D;
    lint M = (lint)(ceil(sqrt(C+0.0)));
    lint K = mod_exp ( A, M, C );
    for ( tmp = 1, i = 0; i <= M; tmp = tmp * A % C, i++ )
        Insert ( i, tmp );

    for ( D = 1, i = 0; i <= M; i++ )
    {
        ext_gcd ( D, C, x, y );
        tmp = ((x * B) % C + C) % C;
        if ( (y = Find(tmp)) != -1 )
            return i * M + y;
        D = D * K % C;
    }
    return -1;
}

int main()
{
    lint P, B, N;
    while (scanf("%I64d%I64d%I64d",&P,&B,&N)!=EOF )
    {
        memset(flag,0,sizeof(flag));
        lint ret = BabyStep_GiantStep (B,N,P);
        if ( ret == -1 ) printf("no solution\n");
        else printf("%I64d\n",ret);
    }
    return 0;
}

下面是HDU 2815 的代码：

#include<cstdio>
#include<cmath>
#include<cstring>
using namespace std;

//BabyStep_GiantStep解决离散对数问题
#define lint __int64
#define MAXN 131071
struct HashNode { lint data, id, next; };
HashNode hash[MAXN<<1];
bool flag[MAXN<<1]; //flag[i] == 0,表示位置i没有放入元素
lint top; //用于解决冲突

void Insert ( lint a, lint b )
{
    lint k = b & MAXN;
    if ( flag[k] == false )
    {
        flag[k] = true;
        hash[k].next = -1;
        hash[k].id = a;
        hash[k].data = b;
        return;
    }
    while( hash[k].next != -1 )
    {
        if( hash[k].data == b ) return;
        k = hash[k].next;
    }
    if ( hash[k].data == b ) return;
    hash[k].next = ++top;
    hash[top].next = -1;
    hash[top].id = a;
    hash[top].data = b;
}

lint Find ( lint b )
{
    lint k = b & MAXN;
    if( flag[k] == false ) return -1;
    while ( k != -1 )
    {
        if( hash[k].data == b ) return hash[k].id;
        k = hash[k].next;
    }
    return -1;
}

lint gcd ( lint a, lint b )
{
    return b ? gcd ( b, a % b ) : a;
}

lint ext_gcd (lint a, lint b, lint& x, lint& y )
{
    lint t, ret;
    if ( b == 0 )
    {
        x = 1, y = 0;
        return a;
    }
    ret = ext_gcd ( b, a % b, x, y );
    t = x, x = y, y = t - a / b * y;
    return ret;
}

lint mod_exp ( lint a, lint b, lint n )
{
    lint ret = 1;
    a = a % n;
    while ( b >= 1 )
    {
        if( b & 1 )
            ret = ret * a % n;
        a = a * a % n;
        b >>= 1;
    }
    return ret;
}

lint BabyStep_GiantStep ( lint A, lint B, lint C )
{
    top = MAXN;  B %= C;
    lint tmp = 1, i;
    for ( i = 0; i <= 100; tmp = tmp * A % C, i++ )
        if ( tmp == B % C ) return i;

    lint D = 1, cnt = 0;
    while( (tmp = gcd(A,C)) !=1 )
    {
        if( B % tmp ) return -1;
        C /= tmp;
        B /= tmp;
        D = D * A / tmp % C;
        cnt++;
    }

    lint M = (lint)ceil(sqrt(C+0.0));
    for ( tmp = 1, i = 0; i <= M; tmp = tmp * A % C, i++ )
        Insert ( i, tmp );

    lint x, y, K = mod_exp( A, M, C );
    for ( i = 0; i <= M; i++ )
    {
        ext_gcd ( D, C, x, y ); // D * X = 1 ( mod C )
        tmp = ((B * x) % C + C) % C;
        if( (y = Find(tmp)) != -1 )
            return i * M + y + cnt;
        D = D * K % C;
    }
    return -1;
}


int main()
{
    int A,B,C;
    while(scanf("%d%d%d",&A,&C,&B)!=EOF)
    {
        if(B>=C){puts("Orz,I can’t find D!");continue;}
        memset(flag,0,sizeof(flag));
        int tmp=BabyStep_GiantStep(A,B,C);
        if(tmp<0)puts("Orz,I can’t find D!");
        else printf("%d\n",tmp);
    }
    return 0;
}